As a first a hearty welcome to the forum. Just realized you're an old user with a new login. 
The place to be for any question regarding Elive. 
Elive has multiple screens covered for a very long time and here's a screenshot of how that works:
from:
Admittedly, I have no personal experience with a Thunderbolt Port but am fairly certain "arandr" has that covered too.
Yes, just run the live version without installing (yet) and see how it functions. 
